Смекни!
smekni.com

Решение оптимизационной задачи линейного программирования (стр. 7 из 7)

+----------------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦ X10 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 2¦ E ¦ 0.00¦ -1.50¦ -2.00¦ 0.00¦ -4.50¦ -2.00¦ 0.00¦ 0.00¦ 0.50¦ 0.00¦ 0.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+-

¦ ¦ -W ¦ 0.00¦ -1.00¦ 2.00¦ 0.00¦ -3.00¦ 2.00¦ 0.00¦ 0.00¦ 2.00¦ 0.00¦ 0.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+

¦ ¦ X4 ¦ 0.33¦ -0.17¦ 0.00¦ 1.00¦ -0.50¦ 0.00¦ 0.00¦ 0.00¦ 0.17¦ 0.00¦ 0.00¦

¦ ¦ X10¦ 0.00¦ 1.00¦ -2.00¦ 0.00¦ 3.00¦ -2.00¦ 0.00¦ 0.00¦ -1.00¦ 1.00¦ 0.00¦

¦ ¦ X7 ¦ 1.00¦ 1.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 8.00¦

¦ ¦ X8 ¦ -0.33¦ 0.17¦ 0.00¦ 0.00¦ 1.50¦ 1.00¦ 0.00¦ 1.00¦ -0.17¦ 0.00¦ 8.00¦

+----------------------------------------------------------------------------------------------------------+

Ведущий элемент находится в 5 столбце и 2 строке.

Вывод промежуточных результатов оптимизации.

+----------------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦ X10 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 3¦ E ¦ 0.00¦ 0.00¦ -5.00¦ 0.00¦ 0.00¦ -5.00¦ 0.00¦ 0.00¦ -1.00¦ 1.50¦ 0.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+

¦ ¦ -W ¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 1.00¦ 0.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+

¦ ¦ X4 ¦ 0.33¦ 0.00¦ -0.33¦ 1.00¦ 0.00¦ -0.33¦ 0.00¦ 0.00¦ 0.00¦ 0.17¦ 0.00¦

¦ ¦ X5 ¦ 0.00¦ 0.33¦ -0.67¦ 0.00¦ 1.00¦ -0.67¦ 0.00¦ 0.00¦ -0.33¦ 0.33¦ 0.00¦

¦ ¦ X7 ¦ 1.00¦ 1.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 8.00¦

¦ ¦ X8 ¦ -0.33¦ -0.33¦ 1.00¦ 0.00¦ 0.00¦ 2.00¦ 0.00¦ 1.00¦ 0.33¦ -0.50¦ 8.00¦

+----------------------------------------------------------------------------------------------------------+

Вывод промежуточных результатов оптимизации.

+----------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+---

¦ 3¦ E ¦ 0.00¦ 0.00¦ -5.00¦ 0.00¦ 0.00¦ -5.00¦ 0.00¦ 0.00¦ 0.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+-

¦ ¦ X4 ¦ 0.33¦ 0.00¦ -0.33¦ 1.00¦ 0.00¦ -0.33¦ 0.00¦ 0.00¦ 0.00¦

¦ ¦ X5 ¦ 0.00¦ 0.33¦ -0.67¦ 0.00¦ 1.00¦ -0.67¦ 0.00¦ 0.00¦ 0.00¦

¦ ¦ X7 ¦ 1.00¦ 1.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 8.00¦

¦ ¦ X8 ¦ -0.33¦ -0.33¦ 1.00¦ 0.00¦ 0.00¦ 2.00¦ 0.00¦ 1.00¦ 8.00¦

+----------------------------------------------------------------------------------------+

Ведущий элемент находится в 3 столбце и 3 строке.

Вывод промежуточных результатов оптимизации.

+----------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+---

¦ 4¦ E ¦ 5.00¦ 5.00¦ 0.00¦ 0.00¦ 0.00¦ -5.00¦ 5.00¦ 0.00¦ 40.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ ¦ X4 ¦ 0.67¦ 0.33¦ 0.00¦ 1.00¦ 0.00¦ -0.33¦ 0.33¦ 0.00¦ 2.67¦

¦ ¦ X5 ¦ 0.67¦ 1.00¦ 0.00¦ 0.00¦ 1.00¦ -0.67¦ 0.67¦ 0.00¦ 5.33¦

¦ ¦ X3 ¦ 1.00¦ 1.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 8.00¦

¦ ¦ X8 ¦ -1.33¦ -1.33¦ 0.00¦ 0.00¦ 0.00¦ 2.00¦ -1.00¦ 1.00¦ 0.00¦

+----------------------------------------------------------------------------------------+

Ведущий элемент находится в 6 столбце и 4 строке.

Вывод промежуточных результатов оптимизации.

+----------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+---

¦ 5¦ E ¦ 1.67¦ 1.67¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 2.50¦ 2.50¦ 40.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ ¦ X4 ¦ 0.44¦ 0.11¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ 0.17¦ 0.17¦ 2.67¦

¦ ¦ X5 ¦ 0.22¦ 0.56¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.33¦ 0.33¦ 5.33¦

¦ ¦ X3 ¦ 1.00¦ 1.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 8.00¦

¦ ¦ X6 ¦ -0.67¦ -0.67¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ -0.50¦ 0.50¦ 0.00¦

+----------------------------------------------------------------------------------------+

Результаты оптимизации.

Базис Значение

X4 2.67

X5 5.33

X3 8.00

X6 0.00

Максимум функции равен 40.00

Вывод промежуточных результатов оптимизации.

+-------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+---

¦ 1¦ E ¦ 1.67¦ 1.67¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 2.50¦ 2.50¦ 0.00¦ 40.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+-

¦ ¦ X4 ¦ 0.44¦ 0.11¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ 0.17¦ 0.17¦ 0.00¦ 2.67¦

¦ ¦ X5 ¦ 0.22¦ 0.56¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.33¦ 0.33¦ 0.00¦ 5.33¦

¦ ¦ X3 ¦ 1.00¦ 1.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ 8.00¦

¦ ¦ X6 ¦ -0.67¦ -0.67¦ 0.00¦ 0.00¦ 0.00¦ 1.00¦ -0.50¦ 0.50¦ 0.00¦ 0.00¦

¦ ¦ X9 ¦ -0.44¦ -0.11¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ -0.17¦ -0.17¦ 1.00¦ -0.67¦

+-------------------------------------------------------------------------------------------------+

Ведущий элемент находится в 1 столбце и 5 строке.

Вывод промежуточных результатов оптимизации.

+-------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 2¦ E ¦ -0.00¦ 1.25¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 1.88¦ 1.88¦ 3.75¦ 37.50¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ ¦ X4 ¦ -0.00¦ -0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ -0.00¦ -0.00¦ 1.00¦ 2.00¦

¦ ¦ X5 ¦ -0.00¦ 0.50¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.25¦ 0.25¦ 0.50¦ 5.00¦

¦ ¦ X3 ¦ -0.00¦ 0.75¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 0.62¦ -0.38¦ 2.25¦ 6.50¦

¦ ¦ X6 ¦ -0.00¦ -0.50¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ -0.25¦ 0.75¦ -1.50¦ 1.00¦

¦ ¦ X1 ¦ 1.00¦ 0.25¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.38¦ 0.38¦ -2.25¦ 1.50¦

+-------------------------------------------------------------------------------------------------+

Результаты оптимизации.

Базис Значение

X4 2.00

X5 5.00

X3 6.50

X6 1.00

X1 1.50

Максимум функции равен 37.50

Вывод промежуточных результатов оптимизации.

+----------------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦ X10 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 2¦ E ¦ -0.00¦ 1.25¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 1.88¦ 1.88¦ 3.75¦ 0.00¦ 37.50¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+-

¦ ¦ X4 ¦ -0.00¦ -0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ -0.00¦ -0.00¦ 1.00¦ 0.00¦ 2.00¦

¦ ¦ X5 ¦ -0.00¦ 0.50¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.25¦ 0.25¦ 0.50¦ 0.00¦ 5.00¦

¦ ¦ X3 ¦ -0.00¦ 0.75¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 0.62¦ -0.38¦ 2.25¦ 0.00¦ 6.50¦

¦ ¦ X6 ¦ -0.00¦ -0.50¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ -0.25¦ 0.75¦ -1.50¦ 0.00¦ 1.00¦

¦ ¦ X1 ¦ 1.00¦ 0.25¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.38¦ 0.38¦ -2.25¦ 0.00¦ 1.50¦

¦ ¦ X10¦ 0.00¦ -0.25¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ -0.38¦ -0.38¦ -2.25¦ 1.00¦ -0.50¦

+----------------------------------------------------------------------------------------------------------+

Ведущий элемент находится в 9 столбце и 6 строке.

Вывод промежуточных результатов оптимизации.

+----------------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦ X10 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 3¦ E ¦ -0.00¦ 0.83¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 1.25¦ 1.25¦ -0.00¦ 1.67¦ 36.67¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+-

¦ ¦ X4 ¦ -0.00¦ -0.11¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ -0.17¦ -0.17¦ -0.00¦ 0.44¦ 1.78¦

¦ ¦ X5 ¦ -0.00¦ 0.44¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.17¦ 0.17¦ -0.00¦ 0.22¦ 4.89¦

¦ ¦ X3 ¦ -0.00¦ 0.50¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 0.25¦ -0.75¦ -0.00¦ 1.00¦ 6.00¦

¦ ¦ X6 ¦ -0.00¦ -0.33¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ -0.00¦ 1.00¦ -0.00¦ -0.67¦ 1.33¦

¦ ¦ X1 ¦ 1.00¦ 0.50¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.75¦ 0.75¦ -0.00¦ -1.00¦ 2.00¦

¦ ¦ X9 ¦ -0.00¦ 0.11¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.17¦ 0.17¦ 1.00¦ -0.44¦ 0.22¦

+----------------------------------------------------------------------------------------------------------+

Результаты оптимизации.

Базис Значение

X4 1.78

X5 4.89

X3 6.00

X6 1.33

X1 2.00

X9 0.22

Максимум функции равен 36.67

Вывод промежуточных результатов оптимизации.

+-------------------------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦ X10 ¦ X11 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 3¦ E ¦ -0.00¦ 0.83¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 1.25¦ 1.25¦ -0.00¦ 1.67¦ 0.00¦ 36.67¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+-

¦ ¦ X4 ¦ -0.00¦ -0.11¦ 0.00¦ 1.00¦ 0.00¦ 0.00¦ -0.17¦ -0.17¦ -0.00¦ 0.44¦ 0.00¦ 1.78¦

¦ ¦ X5 ¦ -0.00¦ 0.44¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ 0.17¦ 0.17¦ -0.00¦ 0.22¦ 0.00¦ 4.89¦

¦ ¦ X3 ¦ -0.00¦ 0.50¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 0.25¦ -0.75¦ -0.00¦ 1.00¦ 0.00¦ 6.00¦

¦ ¦ X6 ¦ -0.00¦ -0.33¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ -0.00¦ 1.00¦ -0.00¦ -0.67¦ 0.00¦ 1.33¦

¦ ¦ X1 ¦ 1.00¦ 0.50¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.75¦ 0.75¦ -0.00¦ -1.00¦ 0.00¦ 2.00¦

¦ ¦ X9 ¦ -0.00¦ 0.11¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.17¦ 0.17¦ 1.00¦ -0.44¦ 0.00¦ 0.22¦

¦ ¦ X11¦ 0.00¦ -0.44¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ -0.17¦ -0.17¦ 0.00¦ -0.22¦ 1.00¦ -0.89¦

+-------------------------------------------------------------------------------------------------------------------+

Ведущий элемент находится в 2 столбце и 7 строке.

Вывод промежуточных результатов оптимизации.

+-------------------------------------------------------------------------------------------------------------------+

¦ N¦ БП ¦ X1 ¦ X2 ¦ X3 ¦ X4 ¦ X5 ¦ X6 ¦ X7 ¦ X8 ¦ X9 ¦ X10 ¦ X11 ¦Баз.Реш.¦

+--+----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--

¦ 4¦ E ¦ -0.00¦ -0.00¦ 0.00¦ 0.00¦ 0.00¦ 0.00¦ 0.94¦ 0.94¦ -0.00¦ 1.25¦ 1.88¦ 35.00¦

¦ +----+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+

¦ ¦ X4 ¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ -0.00¦ -0.00¦ -0.12¦ -0.12¦ -0.00¦ 0.50¦ -0.25¦ 2.00¦

¦ ¦ X5 ¦ -0.00¦ -0.00¦ 0.00¦ 0.00¦ 1.00¦ 0.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ 4.00¦

¦ ¦ X3 ¦ -0.00¦ -0.00¦ 1.00¦ 0.00¦ 0.00¦ 0.00¦ 0.06¦ -0.94¦ -0.00¦ 0.75¦ 1.13¦ 5.00¦

¦ ¦ X6 ¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 1.00¦ 0.12¦ 1.12¦ -0.00¦ -0.50¦ -0.75¦ 2.00¦

¦ ¦ X1 ¦ 1.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.56¦ 0.56¦ -0.00¦ -1.25¦ 1.12¦ 1.00¦

¦ ¦ X9 ¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.12¦ 0.12¦ 1.00¦ -0.50¦ 0.25¦ 0.00¦

¦ ¦ X2 ¦ -0.00¦ 1.00¦ -0.00¦ -0.00¦ -0.00¦ -0.00¦ 0.38¦ 0.38¦ -0.00¦ 0.50¦ -2.25¦ 2.00¦

+-------------------------------------------------------------------------------------------------------------------+

Результаты оптимизации.

Базис Значение

X4 2.00

X5 4.00

X3 5.00

X6 2.00

X1 1.00

X9 0.00

X2 2.00

Максимум функции равен 35.00